US6560295B1 - Method of generating space-time codes for generalized layered space-time architectures - Google Patents
Method of generating space-time codes for generalized layered space-time architectures Download PDFInfo
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- US6560295B1 US6560295B1 US09/613,607 US61360700A US6560295B1 US 6560295 B1 US6560295 B1 US 6560295B1 US 61360700 A US61360700 A US 61360700A US 6560295 B1 US6560295 B1 US 6560295B1
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0056—Systems characterized by the type of code used
- H04L1/0059—Convolutional codes
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/02—Arrangements for detecting or preventing errors in the information received by diversity reception
- H04L1/06—Arrangements for detecting or preventing errors in the information received by diversity reception using space diversity
- H04L1/0618—Space-time coding
- H04L1/0637—Properties of the code
- H04L1/065—Properties of the code by means of convolutional encoding
Definitions
- the invention relates generally to generating codes for use in layered space-time architectures.
- the wireless channel suffers from multi-path fading. In such fading environments, reliable communication is made possible only through the use of diversity techniques in which the receiver is afforded multiple replicas of the transmitted signal under varying channel conditions.
- rate k/n convolutional codes are provided for layered space-time architectures (e.g., rates higher than or equal to 1/n where n is the number of transmit antennas).
- convolutional codes for layered space-time architectures are generated using matrices over the ring F[[D]] of formal power series in variable D.
- FIG. 1 is a block diagram of a multiple antenna wireless communication system constructed in accordance with an embodiment of the present invention.
- FIG. 1 depicts a multiple antenna communication system 10 with n transmit antennas 18 and m receive antennas 24 .
- the channel encoder 20 accepts input from the information source 12 and outputs a coded stream of higher redundancy suitable for error correction processing at the receiver 16 .
- the encoded output stream is modulated and distributed among the n antennas via a spatial modulator 22 .
- the signal received at each antenna 24 is a superposition of the n transmitted signals corrupted by additive white Gaussian noise and multiplicative fading.
- ⁇ square root over (E s ) ⁇ is the energy per transmitted symbol
- ⁇ t (ij) is the complex path gain from transmit antenna i to receive antenna j at time t
- c t i is the symbol transmitted from antenna i at time t
- n t j is the additive white Gaussian noise sample for receive antenna j at time t.
- the symbols are selected from a discrete constellation ⁇ containing 2 b points.
- the noise samples are independent samples of zero-mean complex Gaussian random variable with variance N 0 /2 per dimension.
- the different path gains ⁇ t (ij) are assumed to be statistically independent.
- the fading model of primary interest is that of a block flat Rayleigh fading process in which the code word encompasses B fading blocks.
- the complex fading gains are constant over one fading block but are independent from block to block.
- the system 10 provides not one, but nm, potential communication links between a transmitter 14 and a receiver 16 , corresponding to each distinct transmit antenna 18 /receive antenna 24 pairing.
- the space-time system 10 of the present invention is advantageous because it exploits these statistically independent, but mutually interfering, communication links to improve communication performance.
- the channel encoder 20 is composite, and the multiple, independent coded streams are distributed in space-time in layers.
- the system 10 is advantageous because the layering architecture and associated signal processing associated therewith allows the receiver 16 to efficiently separate the individual layers from one another and can decode each of the layers effectively.
- there is no spatial interference among symbols transmitted within a layer unlike the conventional space-time code design approach.
- Conventional channel codes can be used while the effects of spatial interference are addressed in the signal processor design. While this strategy reduces receiver complexity compared to the non-layered space-time approach, significant gains are possible without undue complexity when the encoding, interleaving, and distribution of transmitted symbols among different antennas are optimized to maximize spatial diversity, temporal diversity, and coding gain.
- a layer is defined herein as a section of the transmission resources array (i.e., a two-dimensional representation of all available transmission intervals on all antennas) having the property that each symbol interval within the section is allocated to at most one antenna. This property ensures that all spatial interference experienced by the layer comes from outside the layer.
- a layer has the further structural property that a set of spatial and/or temporal cyclic shifts of the layer within the transmission resource array provides a partitioning of the transmission resource array. This allows for a simple repeated use of the layer pattern for transmission of multiple, independent coded streams.
- a layer in an n ⁇ l transmission resource array can be identified by an indexing set L ⁇ I n ⁇ I l having the property that the t-th symbol interval on antenna a belongs to the layer if and only if (a, t) ⁇ L. Then, the formal notion of a layer requires that, if (a, t) ⁇ L and (a′, t′) ⁇ L, then either t ⁇ t′ or a ⁇ a′—i.e., that a is a function of t.
- f i denote the component spatial formatting function, associated with layer L i , which agrees with the composite spatial formatter f regarding the modulation and formatting of the layer elements but which sets all off-layer elements to complex zero.
- f ( ⁇ ( u )) f 1 ( ⁇ 1 ( u 1 ))+ f 2 ( ⁇ 2 ( u 2 ))+ . . . + f n ( ⁇ n ( u n )).
- a space-time code may be defined as an underlying channel code C together with a spatial modulator function f that parses the modulated symbols among the transmit antennas.
- the fundamental performance parameters for space-time codes are (1) diversity advantage, which describes the exponential decrease of decoded error rate versus signal-to-noise ratio (asymptotic slope of the performance curve in a log-log scale); and (2) coding advantage which does not affect the asymptotic slope but results in a shift in the performance curve. These parameters are related to the rank and eigenvalues of certain complex matrices associated with the baseband differences between two modulated code words.
- Algebraic space-time code designs achieving full spatial diversity are made possible by the following binary rank criterion for binary, BPSK-modulated space-time codes:
- x denotes an arbitrary k-tuple of information bits and n ⁇ l. Then satisfies the binary rank criterion, and thus, for BPSK transmission over the quasi-static fading channel, achieves full spatial diversity nm, if and only if M 1 , M 2 , . . . M n have the property that
- This construction is general for any number of antennas and, when generalized, applies to trellis as well as block codes.
- transmit delay diversity in which case the symbol alphabet is 4 , the integers modulo 4
- rate 1/n convolutional codes encompasse.g., the class of rate 1/n convolutional codes with the optimal d free , most of which can be formatted to achieve full spatial diversity.
- L be a layer of spatial span n.
- xM n where x denotes an arbitrary k-tuple of information bits.
- f L denote the spatial modulator having the property that the modulated symbols ⁇ (xM j ) associated with xM j are transmitted in the l/b symbol intervals of L that are assigned to antenna j.
- the space-time code in a communication system with n transmit antennas and m receive antennas, the space-time code consisting of C and f L achieves spatial diversity dm in a quasi-static fading channel if and only if d is the largest integer such that M 1 , M 2 , . . . , M n have the property that
- M [a 1 M 1 a 2 M 2 . . . a n M n ] is of rank k over the binary field.
- the natural space-time codes associated with binary, rate 1/n, convolutional codes with periodic bit interleaving are advantageous for the layered space-time architecture as they can be easily formatted to satisfy the generalized layered stacking construction.
- These convolutional codes have been used for a similar application, that is, the block erasure channel.
- the main advantage of such codes is the availability of computationally efficient, soft-input/soft-output decoding algorithms.
- the prior literature on space-time trellis codes treats only the case in which the underlying code has rate 1/n matched to the number of transmit antennas.
- the treatment includes the case of rate k/n convolutional codes constructed by puncturing an underlying rate 1/n convolutional code.
- the output sequence corresponding to Y j (D) is assigned to the j-th transmit antenna.
- F l (D) [G 1,l (D) G 2,l (D) . . . G n,l (D)] T .
- the following theorem relates the spatial diversity of the natural space-time code associated with C to the rank of certain matrices over the ring [[D]] of formal power series in D.
- Rate 1/n′ convolutional codes with n′ ⁇ n can also be put into this framework. This is shown by the following example.
- the design of generalized layered space-time codes that exploit the spatial diversity over quasi-static fading channels has been discussed.
- the results obtained for generalized layered space-time code design are easily extended to the more general block fading channel.
- the quasi-static fading channel under consideration can be viewed as a block fading channel with receive diversity, where each fading block is represented by a different antenna.
- the layered architecture with n transmit antennas and a quasi-static fading channel there are n independent and non-interfering fading links per code word that can be exploited for transmit diversity by proper code design.
- multi-stacking construction is a direct generalization of Theorem 3 to the case of a block fading channel.
- special cases of the multi-stacking construction are given by the natural space-time codes associated with rate k/n convolutional codes in which various arms from the convolutional encoder are assigned to different antennas and fading blocks (in the same way that Theorem 5 is a specialization of Theorem 3).
- Theorem 6 (Generalized Layered Multi-Stacking Construction) Let L be a layer of spatial span n. Given binary matrices M 1,1 , M 2,1 , . . . , M n,1 , . . . , M 1,B , M 2,B , . . . , M n,B of dimension k ⁇ l, let C be the binary code of dimension k consisting of all code words of the form
- x denotes an arbitrary k-tuple of information bits
- B is the number of independent fading blocks spanning one code word.
- f L denote the spatial modulator having the property that ⁇ (xM j,v ) is transmitted in the symbol intervals of L that are assigned to antenna j in the fading block v.
- the space-time code in a communication system with n transmit antennas and m receive antennas, the space-time code consisting of C and f L achieves spatial diversity dm in a B-block fading channel if and only if d is the largest integer such that M 1,1 , M 2,1 , . . . , M n,B have the property that
- M [a 1,1 M 1,1 a 2,1 M 2,1 . . . a n,B M n,B ] is of rank k over the binary field.
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US09/613,607 US6560295B1 (en) | 1999-09-15 | 2000-07-11 | Method of generating space-time codes for generalized layered space-time architectures |
US10/430,002 US7012967B2 (en) | 1999-09-15 | 2003-05-06 | Method of generating space-time codes for generalized layered space-time architectures |
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US09/613,607 US6560295B1 (en) | 1999-09-15 | 2000-07-11 | Method of generating space-time codes for generalized layered space-time architectures |
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US7012967B2 (en) | 2006-03-14 |
US20030194022A1 (en) | 2003-10-16 |
EP1085688A2 (en) | 2001-03-21 |
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